CALCULATION OF GAUSSIAN INTEGRALS USING SYMBOLIC MANIPULATION

The calculation of molecular integrals is extremely important for appl ications to such diverse areas as statistical mechanics and quantum ch emistry. A careful derivation of a method for calculating primitive Ga ussian integrals originally proposed by Obara and Saika is presented. The basic recursion relations for the two- and three-center overlap in tegrals is derived using a simple technique. Several new horizontal re cursion relations are given. Finally, an innovative method for impleme nting these recursion relations is discussed. The recursion relations in this form are suited for programming using a symbolic manipulation language. There are several reasons why it is of interest to consider programming with symbolic manipulation. It has been found that it is p ossible to write algorithms that will generate values for Gaussian int egrals for very large values of angular momentum automatically. Calcul ations can be done to arbitrary precision in Maple. Having these recur sions programmed in Maple allows for the possibility of using the Mapl e programs to help in the writing of similar programs in other languag es which are, numerically, much faster. (C) 1997 John Wiley & Sons, In c.